Studying for their prelim grad school exams, ES & DR were testing each other on memorized values of fundamental physical quantities: the gravitational constant, electron charge, Boltzmann's constant, speed of light, etc. I walked by and ES asked, "What's Planck's constant?"

"One!" I replied, "in appropriate units." It seemed funny at the time (we were under a lot of pressure) but it was also true. By the right choice of dimensions --- length, time, charge, mass, and so forth --- it's possible to make many constants of nature equal any (positive, non-zero) numerical value you please. Do that artfully and the result is simpler, easier-to-manipulate equations.

There are exceptions, dimensionless constants that have no knobs to adjust; they just are what they are. The fine-structure constant, for instance, is about 1/137.036 and governs atomic spectra. The electron/proton mass ratio is another, with a value around 1/1836. No amount of finagling with units can change them --- they're pure numbers.